Mathematical Modelling with Case Studies: A Differential Equations Approach using Maple and MATLAB, Second Edition(Textbooks in Mathematics)

Focusing on growth and decay processes, interacting populations, and heating/cooling problems, Mathematical Modelling with Case Studies: A Differential Equations Approach using Maple™ and MATLAB®, Second Edition presents mathematical techniques applicable to models involving differential equations that describe rates of change. Although the authors concentrate on models involving differential equations, the ideas used can be applied to many other areas. The book carefully details the process of constructing a model, including the conversion of a seemingly complex problem into a much simpler one. It uses flow diagrams and word equations to aid in the model building process and to develop the mathematical equations. Employing theoretical, graphical, and computational tools, the authors analyze the behavior of the models under changing conditions. They discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model. Through applications and the tools of Maple™ and MATLAB®, this textbook provides hands-on model building skills. It develops, extends, and improves simple models as well as interprets the results.

Table of Contents:
Introduction to Mathematical Modeling Mathematical models An overview of the book Some modeling approaches Modeling for decision making Compartmental Models Introduction Exponential decay and radioactivity Case study: detecting art forgeries Case study: Pacific rats colonize New Zealand Lake pollution models Case study: Lake Burley Griffin Drug assimilation into the blood Case study: dull, dizzy, or dead? Cascades of compartments First-order linear DEs Equilibrium points and stability Case study: money, money, money makes the world go around Models of Single Populations Exponential growth Density-dependent growth Limited growth with harvesting Case study: anchovy wipe-out Case study: how can 2 × 106 birds mean rare? Discrete population growth and chaos Time-delayed regulation Case study: Australian blowflies Numerical Solution of Differential Equations Introduction Basic numerical schemes Computer implementation using Maple and MATLAB Instability Discussion Interacting Population Models Introduction An epidemic model for influenza Predators and prey Case study: Nile Perch catastrophe Competing species Case study: aggressive protection of lerps and nymphs Model of a battle Case study: rise and fall of civilizations Phase-Plane Analysis Introduction Phase-plane analysis of epidemic model Analysis of a battle model Analysis of a predator-prey model Analysis of competing species models The predator-prey model revisited Case study: bacteria battle in the gut Linearization Analysis Introduction Linear theory Applications of linear theory Nonlinear theory Applications of nonlinear theory Some Extended Population Models Introduction Case study: competition, predation, and diversity Extended predator-prey model Case study: lemming mass suicides? Case study: prickly pear meets its moth Case study: geese defy mathematical convention Case study: possums threaten New Zealand cows Formulating Basic Heat Models Introduction Some basic physical laws Model for a hot water heater Heat conduction and Fourier’s law Heat conduction through a wall Radial heat conduction Heat fins Solving Time-Dependent Heat Problems The cooling coffee problem revisited The water heater problem revisited Case study: it’s hot and stuffy in the attic Spontaneous combustion Case study: fish and chips explode Solving Heat Conduction Problems Boundary condition problems Heat loss through a wall Case study: double glazing: what’s it worth? Insulating a water pipe Cooling a computer chip Introduction to Partial Differential Equations The heat conduction equation Oscillating soil temperatures Case study: detecting land mines Lake pollution revisited Appendix A: Differential Equations Properties of differential equations Solution by inspection First-order separable equations First-order linear equations Homogeneous equations Inhomogeneous equations Appendix B: Further Mathematics Linear algebra Partial derivatives and Taylor expansions Review of complex numbers Hyperbolic functions Integration using partial fractions Appendix C: Notes on Maple and MATLAB Brief introduction to Maple Using Maple to solve DEs Brief introduction to MATLAB Appendix D: Units and Scaling Scaling differential equations SI Units References Index Exercises appear at the end of each chapter.

About the Author :
University of Technology, Brisbane, Australia Australian National University, Canberra, Australia

Review :
"The book is written in a very lucid manner, with numerous case studies and examples thoroughly discussed. The material is very well organized, generously illustrated, and delightfully presented. All chapters, except the first one, conclude with scores of nicely designed exercises that can be used for independent study. The book contains enough material to organize a new well-structured one-semester course or to complement the existing one with additional examples and problems and is highly recommended for either purpose" --Zentralblatt MATH, 1168 "! The book can be useful for students of mathematical modeling. They will find many skills for modeling and solving real problems. Useful sheets for Maple and MATLAB are included for numerical solution. The most important feature of the book is that it contains many real-life examples. ! The main examples are solved in detail and the others are left for the reader. This is the best treasury of real case problems seen in a single book." --EMS Newsletter, September 2009